Question

The numerator of fraction is 1 less than its denominator . If the numerator is increased by 4 and the denominator is increased by 5 the new fraction becomes equivalent to 4/5 .What is the original fraction ?​

Answer 1

Answer:

let numrator be x-1

denominator=x

num=

increased by 4

den= decreased by 5

then

New no= x_1+4/x_5=4/5

x+3/x_5=4/5

5x+15=4x_20

5x_4x=_20_15

x=_35

num=

Explanation:

No=_36

deno=-35

Answer 2

Given :-

• The numerator of fraction is 1 less than its denominator.

•If the numerator is increased by 4 and the denominator is increased by 5 the new fraction becomes equivalent to 4/5.

To Find :-

• What's the original fraction?

Solution :-

Let the numerator and denominator of the fraction be x and y respectively.

As per question :-

Given that,

The numerator of fraction is 1 less than its denominator.

Therefore,

x = y−1................eq(1)

Again, it’s given that

If the numerator is increased by 4 and the denominator is increased by 5 the new fraction becomes equivalent to 4/5.

Therefore,

(x + 4) / ( y + 5) = 4/5

⟼ 5x +20 = 4y +20

⟼ 5x - 4y = 0........eq(2)

Substitute x = y - 1 in eq(2)

5x - 4y = 0

⟼ 5 ( y -1) - 4y =0

⟼ 5y - 5 - 4y = 0

⟼ y = 5

Now, put the value of y in eq(1)

x = y -1

⟼ x = 5 - 1

$⟼x = 4$

Hence, denominator of the fraction is = 5

Numerator of the fraction is = 4

We know,

Fraction = Numerator / Denominator

Therefore,

original fraction is = 4/5